The invention is based on an arrangement having a module for installation in a bumper of a motor vehicle according to the species of the main claim. It is already known to build modules into a bumper which are configured, for example, as ultrasonic sensors for measuring distance. In this context, the housing of the module is inserted into a corresponding bore of the bumper and is secured there. For influencing the detection range, a baffle plate is then additionally attached which partially covers the ultrasonic sensor. An arrangement of this type is known, for example, from German Patent No. 39 39 387. This arrangement, for design reasons, is not entirely desirable since the parts of the module are configured to be raised with respect to the bumper blade and as a result detract from the appearance. In addition, a sensor of this type is relatively conspicuous so that it can easily be damaged, particularly by children at play.